The combined gross domestic product of the "CTPP ex-U.S." agreement amounts to $12.6 trillion, or 15.8 percent of world GDP. The TPP agreement, which collapsed after the United States pulled out, would have totaled $32 trillion in GDP, or 40 percent.

Still, the new deal without the United States will create a counter-balance to China's increasing economic dominance of the region.

Japanese Prime Minister Shinzo Abe and Australian Prime Minister Malcolm Turnbull led the creation of the new Pacific trade bloc. The administration of U.S. President Donald Trump has largely dropped American leadership on global trade, preferring one-on-one negotiations with other countries.

During his Tuesday appearance at the World Economic Forum in Davos, Switzerland, Canadian Prime Minister Justin Trudeau spent considerable time discussing the merits of international trade.

"If we are going to push back against the anti-trade tendency in globalization that will leave us all worse off, we have to put the concerns and the well-being of our ordinary citizens at the center of what we are negotiating, and that is what 11 of us have been able to do with the CPTPP," Trudeau said.

"We are also very much open to more trade deals involving more people as long as it is in the best benefit of all of our citizens," he said.

On the subject of trade deals still involving the U.S., Trudeau said on Tuesday that Canada is working to persuade Trump that the North American Free Trade Agreement is in the interest of the U.S., Canada and the rest of the world.

"We are working very hard to make sure our neighbor to the south recognizes how good NAFTA is and that it has benefited not just our economy but his economy and the world's economy," Trudeau said.

—CNBC's Ted Kemp and Everett Rosenfeld and Reuters contributed to this report.